I don't have the time to read the whole theory, but I read the first few pages and the diagram doesn't make sense to me. If I understand, the diagram is of the Feynman type, 2d, one space and one time. But space and time as shown by the diagram are not perpendicular. I think it should look like this:

(ignore the dots)
Keep in mind that this is just what came to mind, if the diagram is wrong the math is probably wrong, but I probably misunderstood something. My whole problem with his diagram is that if the time axis is vertical (it is) and we draw objects E0 and E1 at time T, it makes sense that the line connecting p2 and 3 would be horizontal (perpendicular the the space axis), while his clearly isn't.

Before Einstein published the special theory of relativity, the Lorentz transforms were well known. Einstein did not add any new equations (in that publications), he merely gave meaning to the Lorentz transforms.

Diracs matrices are well known and work well in relativistic quantum problems, however no one, including Dirac, has ever been able to give any physical meaning to them. Dirac himsself admitted that many times. He found then basically by mathematical trial and error very much like Lorentz did with his transforms.

What Barwacz has done is not only give them meaning, but also give a new tool to science (a non orthogonal representation of space tiime).

I see my mistake, but how can spacetime be nonorthogonal? Though that would explain why time doesn't seem to be perpendicular to space in my experience, it seems more intangible than that. I already have enough trouble thinking in 4d, I don't think I could add anything else to this forum, nonorthogonal 4d my be the edge of my capablities, sorry.

I can't imagine any method by which we could measure the direction of time relative to space. But if time is change, then it only makes sense that motion (which is a form of change) is the result of projecting a portion of time on to space.

As the Barwacz paper shows, doing so gives simple meaning to time dilation. Also, since the rate of time is fixed at a maximun, it would also clearly explain why nothing can travel faster than light. There simply isn't any more time to project on space.

I can point my fingers in three mutually perpendiular directions, but it take me a million years to come up with the idea that time is perpendicular to the three. I guess it seems that way because moving though time is effortless, and any recognization of time as being like space would just needless confuse me, simplton that I am.

I don't know what your background is, and I haven't read the article you are refering to yet, but I can tell you this. It doesn't make any sense to ask whether time is perpendicular to space or not. Imagine a square and its diagonals. They are perpendicular to one another, but if you move to a velocity v close to the speed of light, c, the square will appear to shrink on your direction of movement (along one of the square's sides). So your square will have become a rectangle, and a rectangle's diagonales are not perpendicular to one another.

The very meaning of a dimension is a perpindicular direction, or degree of freedom that something has. In order for something to be considered a dimension, it must be orthogonal.

For example, consider the space formed by the vectors

a=(1,0,0,0), b=(0,1,0,0), c=(0,0,1,0), t=(0,0,0,1)

To find out these vectors are orthonormal (perpendicular) we must take the inner product space.

<a|b> = &Sigma;ni=1&alpha;i*&beta;i Is the general innerproduct space of vectors a and b. The alpha and beta are merely the coefficients in the vectors a and b repsectively. The * denotes a complex conjugate, which is needed if we are working in the complex space. But here we are not.

Since we have 4 vectors, we wish to check if the vectors are all mutually perpindicular or if they are not.

<a|b|c|d> = &Sigma;ni=1&alpha;i&beta;i&gamma;i&delta;i

In other words the sum of the products of the coefficients of the vectors of the ith term.

So we have 1*0*0*0 + 0*1*0*0 + 0*0*1*0 + 0*0*0*1 = 0. All four vectors have an orthonormal inner product space. Hence we have 4 degrees of freedom, and four dimensions.

However, in quantum mechanics, time is regarded more as a parameter since it lacks a degree of freedom. This can be accounted for by saying that it is perpindicular, but on another space, an imaginary space, and is hence why one often sees the time dimension as a negative quantity when squared, or with an i next to it.